Absorbing state phase transitions with a non-accessible vacuum

Abstract

We analyze from the renormalization group perspective a universality class of reaction-diffusion systems with absorbing states. It describes models where the vacuum state is not accessible, as the set of reactions $2A\to A$ together with creation processes of the form $A\to nA$ with $n\ge 2$. This class includes the (exactly solvable in one-dimension) {\it reversible} model $2A\leftrightarrow A$ as a particular example, as well as many other {\it non-reversible} reactions, proving that reversibility is not the main feature of this class as previously thought. By using field theoretical techniques we show that the critical point appears at zero creation-rate (in accordance with exact results), and it is controlled by the well known pair-coagulation renormalization group fixed point, with non-trivial exactly computable critical exponents in any dimension. Finally, we report on Monte-Carlo simulations, confirming all field theoretical predictions in one and two dimensions for various reversible and non-reversible models.

6 pages. 3 Figures. Final version as published in J.Stat.Mech

References in corpus (4)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Langevin description of critical phenomena with two symmetric absorbing states
• The non-equilibrium phase transition of the pair-contact process with diffusion
• Towards Classification of Phase Transitions in Reaction--Diffusion Models